4 Comparison of parallaxes and proper motions derived from single- or double-star solutions

It has been stressed (Wielen 1997; Wielen et al. 1999) that the proper motions provided by the Hipparcos catalogue may be systematically in error for long-period binaries (i.e. with P > 3 yr), if those were not recognized as such by the reduction consortia. The orbital motion may then add to the actual proper motion, changing both its direction and modulus. The present sample offers a good opportunity to evaluate the impact of this effect.

Figures 7 and 8 compare the position angle and modulus, respectively, of the Hipparcos proper motion with those derived when account is made of the orbital motion as in the present work. It is clearly apparent that the direction of the proper motion listed in the Hipparcos catalogue is correct, as expected, for orbits with periods less than 3 yr, corresponding to the duration of the Hipparcos mission. The Hipparcos values are the less accurate in the orbital-period range 3 to about 5 yr. The position angle quoted by the Hipparcos catalogue may then be off by several dozens degrees (a good illustration of this situation is offered by the the strong Ba star HIP 110108 in Table 2), though it differs generally by less than $3\sigma$ from the correct value. For longer orbital periods, the orbital motion becomes negligible over the duration of the Hipparcos mission, and the proper motions are again rather well determined in the Hipparcos catalogue. The situation is almost identical for the the proper-motion modulus, except that the error bars now become very large for orbital periods longer than 3 yr. This situation translates the fact that the proper motion and the semi-major axis are strongly correlated (resulting in a large formal uncertainty on the proper motion), because the two motions are difficult to disentangle when the Hipparcos data sampled only a fraction of the orbit. This situation is encountered e.g. for HIP 104785 and 104732 (whose astrometric orbits have not been retained precisely because of the large uncertainty on a₀ introduced by the strong correlation with $\mu$), and results in sometime large differences between the a₀ and $\mu$ values derived from the NDAC, FAST and NDAC+FAST data sets, since they are now very sensitive to the measurement errors.

Figure 9 compares the parallax listed in the Hipparcos catalogue with that derived in the present work, as a function of the orbital period. It turns out that the agreement is good, except for systems with orbital periods close to 1 yr. For those systems, the parallax cannot be accurately derived since the orbital motion and the parallactic motion are strongly entangled. This situation is encountered for HIP 17402, 53763 and 62827. Large error bars at periods different from 1 yr correspond to systems with parallaxes smaller than 3 mas.

A few stars (HIP 8876, 29740, 29099, 32831, 36613) in our sample had negative parallaxes in the Hipparcos catalogue. The parallaxes we derive for these systems are slightly positive ($\varpi '$ was adopted to guarantee that property), but the associated error bar encompasses zero, so that these new parallaxes are just useless.